Binary Stars (continued) ASTR 2120 Sarazin γ Caeli - Binary Star System
Visual Binaries: Types of Binary Stars Spectroscopic Binaries: Eclipsing Binaries: Periodic changes in brightness, stars block one stars close together, seen along orbital plane
Eclipsing Binaries Light Curve time
Eclipsing Binaries Eclipse è i 90 o edge-on 90 o i a cos i < R 1 + R 2
Light Curve Flux vs. time primary secondary Primary eclipse = deeper eclipse Secondary eclipse = shallower eclipse
Primary Eclipse Which star behind at primary eclipse? More luminous? NO! Area lost = area of smaller star = same for both eclipses Equal areas lost L = (area) σ T eff 4 change in area the same
Primary Eclipse Primary eclipse è hotter star behind
Light Curves Eccentricity: e 0 è spacing and duration of eclipses unequal Can determine e, Ω flux flux
Central Eclipses, Circular Orbits For simplicity, consider i = 90 o (central), e = 0 (circular) Only total or annular eclipses Constant area removedè flat bottom to eclipses flux flux
Give radii of stars v = total orbital velocity S = smaller star L = larger star v(t 2 t 1 ) = D S = 2 R S v(t 3 t 1 ) = D L = 2 R L v = 2πa / P Eclipse Timing R S = v(t 2 t 1 )/2 = π a (t 2 t 1 ) / P R L = v(t 3 t 1 )/2 = π a (t 3 t 1 ) / P
Eclipse Fluxes flux smaller star behind larger star behind F 0 F S F S F L F L time
Eclipse Fluxes L = (area)σt 4 = 4π R 2 σt 4 eff = 4πd 2 F blackbody distance constant 4πd 2 F 0 = 4π R L2 σt L 4 + 4π R S2 σt S 4 both stars flux smaller star behind larger star behind F 0 F S F S F L F L time
Eclipse Fluxes F S 4πd 2 F S = 4π R L2 σt L 4 only L star F L 4πd 2 F L = 4π R S2 σt S 4 + 4π (R L 2 R S 2 ) σt L 4
Eclipse Fluxes 4πd 2 F 0 = 4π R L2 σt 4 4 L + 4π R S2 σt S both stars 4πd 2 F L = 4π R S2 σt 4 S + 4π (R 2 L R 2 S ) σt 4 L subtract 4πd 2 (F 0 F L ) = 4πd 2 4 ΔF L = 4π R S2 σt L flux smaller star behind larger star behind F 0 F S F S F L F L time
Eclipse Fluxes 4πd 2 (F 0 F L ) = 4πd 2 ΔF L = 4π R S2 σt L 4 4πd 2 F S = 4π R L2 σt L 4 divide (F 0 F L ) F S = ΔF L F S # = R S % $ R L & ( ' 2 ratio of radii
4πd 2 F 0 = 4π R L2 σt 4 4 L + 4π R S2 σt S both stars 4πd 2 4 F S = 4π R L2 σt L only L star, subtract 4πd 2 4 ΔF S = 4π R S2 σt S 4πd 2 ΔF L = 4π R S2 σt 4 flux L previous, divide ΔF S ΔF L F smaller star behind 0 " = T S $ # T L % ' & F 4 S Eclipse Fluxes F S larger star behind F ratio of temperatures L time F L
Stellar Radii and Temperatures Normal Stars: main sequence, dwarfs 0.1 R < R < 20 R 3000 K < T eff < 50,000 K sequence: small, cool, faint è big, hot, bright Giants: R > 100 R ~ AU cool, T ~ 3000 K White Dwarfs: R 0.01 R ~ R(Earth) observed WDs very hot ~ 100,000 K
Properties of Stars from Binaries Type Observation Properties Determined Visual m 1, m 2, π distance d, luminosities L 1, L 2 P, a, π semimajor axis a, total mass M 1 + M 2 a 1 /a 2 masses M 1, M 2 Spectroscopic Single-line velocity curve mass function f(m 1, M 2, sin i), e, Ω Double-line velocity curve Eclipsing Shape of light curve, spacing of eclipses e, Ω, i, P Duration of eclipses R 1 /a, R 2 /a M 1 /M 2, (M 1 + M 2 ) sin i, e, Ω Depth of eclipses R 2 /R 1, T 2 /T 1 Eclipse & velocity curve a, R 1, R 2, T 1, T 2, M 1, M 2, e, i, Ω, P
The Sun: A Star of Our Own ASTR 2120 Sarazin
Review of Sun Chapter 7 in Text
Sun = A Very Average Star R 8 = 7 x 10 10 cm M 8 = 2 x 10 33 g Average Density <r> = 1.41 g/cm 3 (less than Earth) Sun is mainly hydrogen Composition: 74% Hydrogen, 24% Helium, 2% everything else (by mass)
Age of Sun Radioactive dating Oldest materials in Solar System 4.6 billion years Consistent with age of Sun from stellar theory Age of Sun = 4.6 billion years
Rotation period Equator: 25 days Poles: 30 days Differential rotation Solar Rotation
Where Does Light Come From? Mean-free-path of photons in the Sun ~ 1 cm in the center ~ 400 km at surface Light that we see comes only from surface (from narrow layer) = photosphere (doesn t tell us where energy ultimately comes from)
Photospheric Spectrum
Photospheric Spectrum Continuum emission (all wavelengths) ~ black body Absorption lines
Photospheric Spectrum Wavelengths of lines bigger opacity, smaller mean-free-path Don t see in as far cooler absorption lines hotter continuum emission center
Photospheric Spectrum General result Stellar spectra = continuum emission + absorption lines Temperature in stars increases inwards
Photosphere Chromosphere Solar Atmosphere Hotter 10,000 K Corona Very hot, millions K Extends out very far Solar Wind
Sunspots Prominences Flares Solar Activity Solar Cycle = 11 period, 22 for magnetic field Due to rotation, convection, and magnetic field
Solar Prominence Sep. 14, 1999
Sunspots and Solar Cycle
Charged Particles in Magnetic Fields Helical motion F = q c v B Work = ( ) q = charge F d r = F v dt = 0 E = constant, thus KE = constant v = constant In plane B, circle orbit r g = mv c qb gyro radius v = constant, v = constant Helical motion B
Bulk Properties of Plasma with Magnetic Field Faraday s Law: changing magnetic field electric field current (if conductor) opposite sign Ampere s Law: current magnetic field Acts to prevent change in magnetic field B
Bulk Properties of Plasma with Magnetic Field Can t pull wire from B field Plasma = like wires in all directions Frozen-In Condition Plasma and Magnetic Field are locked together B B wire plasma
Bulk Properties of Plasma with Magnetic Field Frozen-In Condition plasma and magnetic field tied Who is master and who is slave? Bigger pressure wins. Gas pressure P gas = n k T Magnetic pressure P B = B 2 /(8p)